NC Math 2: Transformations Investigation Name # For this investigation, you will work with a partner. You and your partner should take turns practicing the rotations with the stencil. You and your partner must turn in SEPARATE INVESTIGATION AND GRAPH SHEETS to receive credit. Materials: Each pair of students will need the following materials to complete the investigation One ruler. One stencil. This is the circle with the triangle and rectangle cut-outs. Two investigation worksheets, one for you and one for your partner. Two regular pencils. NO PENS. At least 1 colored pencil. Rotations of 90 Degrees Clockwise (1) Draw a rectangle on your graph paper by plotting the following points. A(1, 7), B(3, 7), C(3, 4), and D (1, 4) Be sure to label the points on your graph paper A, B, C, D. A A (2) Place the circle stencil on the graph so that the rectangles line up. Also make sure the number lines overlap. (3) Rotate the circle 90 degrees Clockwise. Be sure that the bold number lines overlap. (4) Draw the new rectangle after the rotation. Use the nearest whole numbers and gridlines to make sure the rectangle is correctly drawn. Use the letters on the stencil to label the points of your new rectangle A, B, C, and D. Be sure A represents A s new location, B B s new location, etc. B B C C D D (5) Use the grid to find the coordinates of the new points of the rectangle. Fill out the data table to the right with the (x, y) points. (6) Using a colored pencil and a ruler, draw a line from Point A to the origin (0, 0). Using the same color, draw a line from point A to the origin. Critical Thinking Questions: Discuss with your partner the following questions in order to make conclusions about 90 degree clockwise rotations. (1) How did the shape of the rectangle change? (2) Look where the lines connecting A and A meet at the origin. They form an angle. Create a hypothesis for what type of angle this is.
(3) What do we know about the slope of lines perpendicular lines that will help us test the hypothesis? Calculate the slope for each AO and A O verify your hypotheses. (4) What connections do you notice between the coordinates of the pre-image points and the image points for the two rectangles? Rotations of 180 Degrees Clockwise (1) Draw a triangle on your graph paper by plotting the following points. E(2, 1), F(5, 3), G(5, 1) Be sure to label the points on your graph paper. E E (2) Place the circle stencil on the graph so that the triangles line up. Also make sure the number lines overlap. (3) Rotate the circle stencil clockwise 180 degrees. (4) Use the circle stencil to draw the location of the triangle after the rotation. Use the letters on the stencil to label the new points E, F, and G. F F G G (5) Use the grid to find the coordinates of the new points of the triangle. Fill out the data table to the right. (6) Using a new colored pencil and a ruler, draw a straight line from point E to the origin (0, 0). Now, draw a line from point E to the origin using the same colored pencil. Critical Thinking Questions: (1) Did the shape of the triangle change? If so, how? (2) Examine the lines connecting E and E to the origin. What happened when the lines met at the origin? What do they form? (3) Using a new colored pencil, draw a straight line from G to G. Did this line also cross the origin? (4) What connections do you notice between the coordinates of the pre-image points and the image points for the two triangles?
(5) Rotate your original triangle 180 degrees counterclockwise. How does a rotation for 180 degrees clockwise compare to 180 degrees counterclockwise? Extending Our Knowledge: For these questions you will use the discoveries you made to solve problems. (1) Think about the patterns you observed for the coordinates of rotations. Do not use the circle. Write down the new (x, y) coordinates for the point (5, 6) after a rotation of : 90 degrees Clockwise 180 degrees Clockwise 180 degrees Counterclockwise 270 degrees Clockwise 90 degrees Counterclockwise 270 degress Counterclockwise (2) Check your work by using the stencil. There is a single hole for the point (5,6). (3) Circle True or False: A rotation of the point J(-4, 7) 180 degrees counterclockwise creates a new point J (-4, -7). Explain. (1) Using your stencil and paper from yesterday, create a horizontal reflections of the triangle across the y-axis by flipping the stencil over in the horizontal direction. Trace the new triangle. Horizontal Reflections (Reflecting across the y-axis) E E (2) What is similar between a horizontal reflection across the y-axis and a 90 degree CCW rotation? What is different? F G F G (3) Write the pre-image and image points for the new triangle is the table to the right. (4) Write a rule to represent how the coordinates of a shape change after a reflection over the y-axis.
(5) Use the rule you created in step 4 to determine the coordinates of the image points for the rectangle. DO NOT USE THE STENCIL YET.just make an educated guess. A A (6) Now, check your answers by using the rectangle on the stencil and reflecting it over the y-axis. How did you do? B C B C Make any necessary changes to your answers in the table. D D (1) Before we do a vertical reflection over the x- axis, what do you think the rule will be? (Make your best guess using what you have learned from the last activity.) Vertical Reflections (Reflecting over the x-axis) E E (2) Using your stencil and paper from yesterday, create a reflection over the x-axis by flipping the stencil over in a vertical direction. Trace the new triangle. (3) What is similar between a reflection across the x-axis and a 90 degree rotation CW? What is different? F G F G (4) Record the pre-image and image points for the new triangle in the table to the right. (5) Was your prediction in step 1 correct? (6) Use your rule to determine the image points for the rectangle. DO NOT USE THE STENCIL YET just make an educated guess. Record your answers in the table to the right. (y) Now, check your answers by using the rectangle on the stencil and reflecting it over the x-axis. A B C A B C How did you do? Make any necessary changes to your answers in the table. D D